The current status of elementary particle physics, with no clear signature of new phenomena appearing at the LHC, no direct detection of Dark Matter (DM) and only a handful of deviations from the Standard Model (SM) predictions, poses a challenge to our community.

To tackle it one can follow different approaches that, while not being the same, are deeply interconnected:

• we need complete theoretical control of the SM, to understand if deviations from the observed data are due to our less-than-optimal computations (and computer simulations) or due to new physics;
• for theoretically motivated extensions of the SM, we should compute with sufficient accuracy the observables that are important for LHC phenomenology (e.g. Higgs mass, W mass, Higgs observables, Higgs differential distributions etc.), where the effect of Beyond Standard Model (BSM) physics could manifest itself. This effort will also allow us to understand what part of the parameter space of a BSM model is still compatible with the LHC measurements. In parallel, We also need to re-appraise the BSM signatures coming from the direct production of new states to understand what it could have been missed with the current searches so far;
• for a consistent analysis, LHC results have to be complemented with the information coming from low-energy physics, flavor observables, dark matter and cosmological observations. Indeed, as the probability of discovering smoking-gun signs of new physics at the LHC diminishes, the importance of considering how new physics appears in other domains aside from collider physics becomes more and more relevant.

Concerning the first point, we can identify two aspects.

On the one side, one might pursue the development of more and more redefined calculations and the development of the corresponding computational tools. My activity here has been mostly focused on the developments of state-of-the-art Monte Carlo event generator in the NLO+PS POWHEG-BOX framework.

On the other side, for the existing calculations and tools, an understanding of all the SM theoretical assumptions and uncertainties is required, both at the analytic-computation level in Quantum Chromodynamics (QCD) (such as, for example the so-called Missing Higher Order Uncertainties (MHOUs)), and in the computational frameworks used to produce the predictions that are eventually compared with the data. In this context, my studies are focused on specific standard model processes, especially the ones connected to the electroweak bosons and to the measurements of SM observables such as the W mass. This activity includes the study of the theoretical uncertainties that affect the Monte Carlo (MC) frameworks used at the LHC (both SM and BSM) or other forms of uncertainties affecting more in general the theory predictions (e.g. PDF uncertainties). More in general new developments are needed for an improved inclusion of MHOUs in our computations, for example by improving the Bayesian models currently available or by developing new ones. Indeed, the reduction in the experimental uncertainties (both statistic and systematic) as the LHC proceeds with its runs makes this kind of studies on the theory uncertainties more relevant and important. This is also an area of development that I deem especially interesting.

With respect to the second item, an improvement in our understanding of BSM signatures could come from new, more precise, studies looking at how new physics can manifest itself in the form of deviations from the SM in those observables that will be deeply scrutinized thanks to the large integrated luminosity that was/will be gathered during LHC Run 2/3, and during HL-LHC operations. A prime target for possible effects is the Higgs sector (couplings, transverse momentum, off-shell production), but other observables, such as precision EW observables and processes (Drell-Yan etc.), could also yield interesting information. Of course, we should also consider the possibility of new signatures which have not been scrutinized yet.

Finally, with regard to the third point, to understand the real compatibility of a BSM model with experimental observations, the only consistent route is to perform a global likelihood analysis of the model, keeping into account all the possible constraints coming from experiments at different energy scales. Therefore, besides looking at exclusion searches for direct production of new states at the LHC, the other important constraints are precision observables such as the Higgs mass or the W mass, flavor observables, $(g-2)_{\mu}$ and, last but not least, the fulfillment of the DM relic density and the constraints coming from DM direct and indirect detection experiments. Combining all this information, in a consistent way, is required to properly assess the allowed parameter space of the model. It also points out to the importance of studying more in detail other domains beyond pure collider physics.

In this regard, in the past few years, I have had firsthand experience in all these areas and I am continuing to be part of ongoing and new collaborations on these topics.

All these research lines can directly thrive by close collaborations with experimentalists – and indeed these are already under way. For example, in the context of the HXSWG, I am collaborating since years with members of the experimental collaborations for the inclusion in their analyses of the results of our studies on how to properly predict the Higgs transverse momentum distribution in the 2HDM and in the MSSM. This work is relevant to correctly assess the acceptance of the detectors in the experimental analyses, when the results are interpreted in terms of a specific model/scenario. A first outcome has been its use in the CMS search for $H/A \to \tau^+ \tau^-$, which has been published in 2019.

In other contexts, the results from our global likelihood analyses allow to understand the current and future reach of experimental searches for specific models, not only for the LHC but also, for instance, for direct detection DM experiments such as LUX, XENON or PandaX.